A good half a mile time is totally good, if a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile.
In the given question, we have to explain, what is a good half a mile time.
First, some background is required for 5:43 for half a mile. When did you start running? Was that time calculated using a full effort, or was it only the distance covered without walking? Don't worry about if it's good if you're spanking new. Use it as a foundation.
Second, like with most things in life, practise makes perfect, and running performance is no exception. If a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile. The goal is to gradually push your boundaries until you consistently cross that threshold and then push your limits even farther.
Your body will be encouraged to adapt to the challenge, grow to it, and become prepared for when the challenge gets harder.
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The graph shows the relationship between the amount of peaches in pounds, x, and the amount of peaches in dollars, y. What is the slope of the line?
Answer: 5/2 or 2.5
Step-by-step explanation: Rise/Run = 5/2
what is surface area of the cuboid 4cm.5cm.9cm.
Answer:202 surface area
Step-by-step explanation:
a company is placing an order for boxed lunches for a meeting of its executive board. there are 10 members of the board and each will have one lunch. the company is getting the lunches from a restaurant that has 25 varieties of boxed lunches. (a) how many different ways are there for the company to place the lunch order for the 10 lunches? note that it is not important who gets what lunch. all that matters is how many of each of the 25 possible varieties are purchased. (b) how many ways are there for the company to place the lunch order if the 10 lunches purchased are all different? (again, who gets what lunch is not important, just how many of each lunch are purchased).
a)
There are 3268760 different ways for the company to place the lunch order for the 10 lunches
b)
There are 11861676288000 ways for the company to place the lunch order if the 10 lunches purchased are all different
What is permutation and combination?
The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics include permutations in some form or another. They frequently appear when various orderings on certain finite sets are taken into account.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations may be counted in simpler situatiThe combinationation is the taking together of n items, k at a time, without repetition. The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
a) total different ways are [tex]C^{25} _{10}[/tex]
= 25!/(25-10)!10!
= 25!/15! * 10!
= 3268760
b) total different ways are [tex]P^{25} _{10}[/tex]
= 25!/(25-10)!
= 25!/15!
= 11861676288000
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You are given an integer n where 0 <= n <= 100, followed by another line of input which has a word w with length l where 1 <= l <= 50. Your task is to print n lines with the word w. The lines of your output should not have any trailing or leading spaces.
The Python program to print the value of the input string is as follows:N= int(input("Enter a integer variable N (0 <= N <= 100): ")), W = input("Enter the word W (length of 1 <= L <= 50): "), for n in range(N):, print(W)
A variable, what exactly do you mean?In a mathematical problem or experiment, a variable is a quantity that can change. To represent a variable, we typically use a single letter. Generic symbols used frequently for variables include the letters x, y, and z.
Program -
N= int(input("Enter a value of integer N (0 <= N <= 100): "))
W = input("Enter the word W (length of 1 <= L <= 50): ")
for n in range(N):
print(W)
Here,
defining the integer variable "N" that accepts a user-supplied integer value.
The user-end string value is input using another variable "W" that is declared in the next step.
A for loop using the range method and an integer variable is declared after all input values have been entered. This loop prints the string value.
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(1 point) how many strings of four decimal digits (note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.)
a) Four-digit strings with 10⁴ characters are available.
b) A string that finishes in an odd number has 10 options for the first three digits and 5 options for the last digit.
c) The fourth digit has nine alternatives.
Given,
We have to find the number of strings of four decimal digits for the following conditions;
a) Do not use the same numeral more than once.
There are 10⁴ strings with four decimal digits.
We have 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit when creating a string with 4 different digits. We deduce from the product rule that there are 10 9 8 7 = 5040 four decimal digits with no duplicate digits.
b) End with an odd digit
There are 10 choices (ranging from 0 to 1, 2,..., 9) for the first three digits of a string that ends in an odd number, and 5 possibilities (ranging from 1, 3, 5, 7,.., 9) for the last digit. According to the product rule, there are 5000 strings that terminate in an even number, or 10 × 10 × 10 × 5.
c) Have exactly three digits that are 8
There is one non-8 digit in the 4-decimal string, which includes exactly 3 digits that are 8. Therefore, there are 9 options for the fourth digit (ranging from 0 through 1, 2, 3, 4, 5, 6, and 9). The non-digit may appear in the string at positions 1, 2, 3, or 4. The sum rule leads us to the conclusion that there are 36 four decimal digits with exactly three 8s, which equals 9 + 9 + 9 + 9 = 36.
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Question is incomplete. Completed question is given below;
How many strings of four decimal digits
a) Do not contain the same digit twice
b) End with an odd digit?
c) Have exactly three digits that are 8
16. Find the direction of the force
F=(-√12 i-2j) N.
Answer:
240° ( Quadrant III)
Step-by-step explanation:
Arctan ( -sqrt(12) /-2) = 240 degrees
solve the inequality
15t>180
Answer: t=12
Step-by-step explanation:
To isolate the t, divide both sides by 15. The 15 on the left cancels out, and 180 divided by 15 is 12.
Your team has contracted to design and build a 500 ft, square-based, open-top, rectangular steal holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible.
The first step is to calculate the approximate weight of the tank. This can be done by calculating the weight of the stainless steel plates and multiplying it by the surface area of the tank.
The surface area can be calculated by multiplying the length of the sides by the height. The weight of the stainless steel plates can be found online or by consulting a materials engineer.Once the approximate weight of the tank has been calculated, the base and height dimensions can be determined by trial and error. Start with a base length and a height and calculate the approximate weight of the tank. Then, adjust the base length and/or height and recalculate the weight. Continue this process until the lightest weight is achieved.It is important to consider the structural integrity of the tank when selecting the dimensions. A tank with too little height or too wide a base may not be able to withstand the pressure of the contents within. Consulting a structural engineer may be necessary to ensure that the tank is strong enough to withstand the pressure of the contents.
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Which of the following is a diagonal matrix?
O
2
0
0 -42
0
0
1
6
0
0
16 -7.5
0
0
3.5 -18
0 9
-4
0
0
0
-22 0
0 7.5
0
0 7.5
0-22 0
Mark this and return
Save and Exit
4
Answer: the second one
Step-by-step explanation: trust me bro
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations? (a) n 15 t 1.66 a 0.05 o Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in o Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
The correct answer is 'Do not reject the null hypothesis as there is not sufficient evidence that the true diameter differs from 0.5 in.'
When the sample size is large and the standard deviation is known, the z-test is typically used.
The T-test is more flexible than the Z-test since the Z-test frequently needs particular circumstances in order to be reliable.
The t test is applied if the population standard deviation is unknown.
Test statistic for one sample t-test is, t = (X‾ - μ0) / (s / √n)
The formula of degrees of freedom for test is, df = n-1 here, n is sample size.
Decision rule:
1. If the P-value is less than the level of significance, the null hypothesis should be rejected; otherwise, it should not be.
2.The null hypothesis is rejected if the t-test statistic value is greater than the t tabulated value; otherwise, the null hypothesis is not rejected.
(a) From the given information, n=15, t=1.66, α =0.05 we can derive
degrees of freedom = df= n-1 which is 15-1 = 14
Thus, the critical value is, 2.145.
Now, since the test statistic value is less than the critical value, do not reject the null hypothesis.
Here, the test statistic value do not lie in the critical region. The null hypothesis cannot be rejected. There is insufficient evidence that the true diameter differs from 0.5 in.
(b) From the given information, n=15, t = -1.66, α =0.05 we can derive
degrees of freedom = df= n-1 which is 15-1 = 14
Thus, the critical value is, -2.145.
Now, since the test statistic value does not lie in the rejection region, do not reject the null hypothesis.
Here, the test statistic value does not lie in the critical region. The null hypothesis cannot be rejected. There is insufficient evidence that the true diameter differs from 0.5 in.
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a coin is weighted so that the probability of obtaining a head in a single toss is 0.25. if the coin is tossed 45 times, what is the probability of obtaining between 9 and 14 heads, exclusive. a. 0.0537 b. 0.5051 c. 0.7201 d. 0.6975 e. 0.4836
The probability of obtaining between 9 and 14 heads is .0.0408
Probability:
in statistics, probability refers the possibility of the outcome of any random event.
Given,
A coin is weighted so that the probability of obtaining a head in a single toss is 0.25.
Here we need to find the probability of obtaining between 9 and 14 heads if the coin is tossed 45 times.
While we looking into the given question,
Probability of obtaining a head in a single toss = 0.25
Number of toss = 45
Here we need to find the probability of getting head between 9 and 14, is calculated as,
=> mean = 45 x 0.25 = 11.25
=> standard deviation = √11.25 x(1 - 0.25) = 2.9
Here the probability is written as,
=> P(9 < x < 14) = P(8.5 < x < 14.5)
Then the z score, is
=> z = (8.5 - 11.25)/2.9 = -0.9483
=> z = (14.5 - 11.25)/2.9 = 1.1207
So, the given probability is rewritten as,
=> P(9 < x < 14) = P(z < 1.1207) - P(z < 0.9483)
When we apply the value of z score on it then we get,
= > P(z < -0.9483) = 0.17149
=> P(z > 1.1207) = 0.13121
=> P(9 < x < 14) = 0.13121 - 0.17149
=> 0.0403
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In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)°, what is the value of x?
O 51
0 29
026
O 25
The value of x, if In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)° is 25, so correct option is D.
What is triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.
Given:
In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)°
Calculate the value of x as shown below,
The sum of triangles will be equal to 180°,
mZD + mZE + mZF = 180
4x + 2x - 3 + x + 8 = 180
7x = 180 - 5
x = 175 / 7
x = 25
Therefore, the value of x, if In triangle DEF, if mZD = (4x)°, mZE = (2x - 3)°, and mZF = (x + 8)° is 25.
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How to solve 3(1+p)=-5(p+1)
The value of P in the equation is -1
Answer:
p=-1
Step-by-step explanation:
3(1+p)=-5(p+1)
Remove the parenthesis:
3+3p=-5p-5
Subtract 3 from both sides.
3p=-5p-5-3
Simplify:
3p=-5p-8
Rearrange:
3p=-8-5p
Add 5p to both sides:
8p=-8
Divide both sides by 8:
p=-1
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let x denote the number of canon slr cameras sold during a particular week by a certain store. the pmf of x is x 0 1 2 3 4 px(x) 0.1 0.2 0.3 0.25 0.15
the value of P(X=4,Y=2) is 0.0518.
Given that, X denote the number of Canon SLR cameras sold during a particular week by a certain store.
The probability mass function (pmf) of X is,
X 0 1 2 3 4
PX(x) 0.1 0.2 0.3 0.25 0.15
Let Y denote the number of purchasers during this week who buy an extended warranty.
The value of P(X=4,Y=2) is the probability that 4 cameras are sold and 2 extended warranties are sold in a week.
P(X=4,Y=2)=p(4,2)=P(Y=2|X=4)×P(X=4)
The number of purchasers purchasing the extended warranty can be 0, 1, ……, x.
Here x is cameras are sold.
Assuming that each customer buys at most 1 camera.
Considering that the event “a purchaser buys extended warranty” as “success” and the event “a purchaser does not buy extended warranty” as “failure”.
In that case, all the customers purchasing cameras buy extended is 60%.
The probability of failure is 0.4.
This follows the binomial distribution, where total number of trials is the number of purchasers of camera and x is the probability of success is 0.6.
The probability that 2 out of 4 cameras purchasers buys extended warranty with probability of success 0.6 is,
P(Y=2|X=4)=4C2(0.6)2(0.4)4−2=6×0.36×0.16=0.3456
Given that,
P(X=4)=0.15
Therefore,
P(X=4,Y=2)=P(Y=2|X=4)×P(X=4)=0.3456×0.15=0.0518
Therefore, the value of
P(X=4,Y=2) is 0.0518.
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Use the number line to represent the solution to 5x > 15
Select a ray. Move the point on the ray to the correct place on the number line.
The solution to the inequality expression is x > 3 and the number line is attached
How to determine the solution to the expression?From the question, we have the following parameters that can be used in our computation:
5x > 15
To start with, we divide both sides of the inequality expression by 5
So, we have the following representation
5x/5 > 15/5
Evaluate the quotient
So, we have the following representation
5x/5 > 3
Evaluate the quotient
So, we have the following representation
x > 3
So, the solution is x > 3
See attachment for the inequality graph
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Calculate the unit rate for each option and determine which one is the BEST buy.
$160 for 10 books
$114 for 6 books
Answer:
$160 for 10 books is the BEST buy.
Step-by-step explanation:
To find which one is the best buy, we need to find the unit rate for the books (which is how much each book is worth). We do this by simply dividing the two numbers in each buy:
160 ÷ 10 = 16
114 ÷ 6 = 19
Since the first one is a smaller price, the first one is our answer.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 3 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
It would be $160 for 10 books
in a class of 3000 students, the professor gives a multiple choice quiz with 4 questions, possible answers a,b,c, d or e. each student answers each question. among the 3000 students, at least how many students will turn in the exact same answers for the quiz questions?
Among the 3000 students, at least 5 students will turn in the exact same answers for the quiz questions.
What does at least mean in probability?
"At least" means as follows: equivalent to or less than. The bare minimum that should happen once a random event occurs is called the least mean in probability.
It will be the complement of the event never occurring to determine the likelihood of an event occurring at least once. In other words, there is a 100% chance that the event will occur regardless of its likelihood of never happening or happening at least once.
Solution Explained:
The quiz has 54=625 different possible outcomes. Given that 625 divided by four equals 2600 and 625 multiplied by five equals 3125, we deduce that 5 students will submit the same set of answers. This is due to the fact that there would be a maximum of 2600 students if only 4 students submitted each answer sheet.
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a dental student is conducting a study on the number of people who visit their dentist regularly. of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
For samples of size n = 60, the mean of the sampling distribution is 0.6
and the standard deviation of the sampling distribution is 0.0632
Here, N = 520 and X = 312
So, the population proportion is calculated as;
p = X / N
p = 312/520
p ≈ 0.600
So, the mean of the sampling distribution would be,
μ = 0.600
And for samples of size n = 60, the standard deviation of the sampling distribution would be,
σ = √[p(1 - p)] / n
σ = √[0.6(1 - 0.4)] / 60
σ = √[(0.6 * 0.4) / 60]
σ = √(0.004)
σ = 0.0632
Therefore, the mean of the sampling distribution = 0.6
and the standard deviation of the sampling distribution = 0.0632
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Given question is incomplete.
A complete question is:
a dental student is conducting a study on the number of people who visit their dentist regularly. of the 520 people surveyed, 312 indicated that they had visited their dentist within the past year. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n = 60
Find the perimeter of a rectangle in simplest expression form that has an area of 6x2 +17x + 12 square feet. Please make sure you show all your work for full credit. (10 points)
Answer: P=14x-8
Step-by-step explanation:
I will solve this by factoring the numbers
(3x+1)(4x-5)=0
so L and w would be 3x+1,4x-5 order does not matter
Plug in to the perimeter formula and solve
P = 2(L+W)
P = 2(4x-5+3x+1)
P = 2(7x-4)
P = 14x - 8
0.25r=0.5 how do i solve this please help.
Answer: r=2
Step-by-step explanation:
do .5/.25=2
Consider the division of 4h2 + 2h + 6 by 2h. What are the values of a and b? a = 2 and b = 1 a = 2h and b = 1 a = and b = a = and b =.
When the dividend is 4h²+2h+6 and the divisor is 2h, the value of a is 2h and the value of b is 1.
What is polynomial?A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. The terms degree, standard form, monomial, binomial, and trinomial are all covered in this video.
Here,
Dividend=4h²+2h+6
Divisor=2h
The value of a and b,
=(4h²+2h+6)/2h
=4h²/2h+2h/2h+6/2h
=2h+1+3/h
a=2h
b=1
The value of a is 2h and b is 1 where the dividend is 4h²+2h+6 and divisor is 2h.
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Answer:What are the values of A and B?
A = 2 and B = 1
A = 2h and B = 1
A = and B =
A = and B =
Step-by-step explanation:
The triangles below are congruent and their corresponding parts are marked.
B
(a) LA = 40
LB = 40
LC = 40
(c) AACB A
X
Z
Name all the corresponding congruent angles and sides.
Then, complete the triangle congruence statement.
(b) AB
AC
BC
X
Ś
Answer:
AB = YZ
AC = XY
BC =XZ
Statement : The given two triangles are congurent by all axiom.
Find the perimeter and area of triangle RST if each unit on the graph measures 1 centimeter. Round your answer to the nearest centimeter, if necessary.
y
8
S-4,5)-6
Q-6,1)
-876
R(-8,-3)
Perimeter
Area
4
-6
81
468x
7(6,-5)
cm²
jcm
The perimeter and the area of the triangle are given as follows:
Perimeter: 21 cm.Area: 16 cm².How to obtain the perimeter of the triangle?The perimeter of the triangle is given by the sum of the lengths of the outer edges of the triangle.
From the image given at the end of the answer, these lengths are of:
AB = 4.AC = 8.BC = 8.83 -> Pythagorean Theorem -> hypotenuse of a right triangle of sides 4 and 8.Hence the perimeter of the triangle is of:
P = 4 + 8 + 8.83 = 21 cm.
(rounded to the nearest cm, as each unit represents 1 cm).
How to obtain the area of the triangle?The triangle in this problem is a right triangle, hence the area is obtained by half the multiplication of the sides, as follows:
A = 0.5 x 4 x 8 = 16 cm².
Missing InformationThe problem is incomplete, hence a similar problem was given and solved, by the triangle in the image at the end of the answer.
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Jade pent 1/2 of an hour playing on her phone. That ued up 1/9 of her batter. How long would he have to play on her phone to ue her entire battery
She has to play 4.5 hours to discharge the whole phone.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Jade spent 1/2 of an hour playing on her phone which uses 1/9th of her battery.
For 1/9th battery, it took 1/2 hour.
So for the whole charge to discharge it will take, (1/2)/ (1/9) = 9/2 =4.5.
Hence, She has to play 4.5 hours to discharge the whole phone.
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I really need someone to help me understand this problem
The linear function in slope intercept form is y = -2x - 5.
How to represent linear function in slope intercept form?Linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope in the linear function.
Using (-1, -3) and (3, - 11)
m = -11 + 3 / 3 + 1
m = -8 / 4
m = -2
Therefore, let's find the y-intercept as follows:
using (-1, -3)
y = -2x + b
-3 = -2(-1) + b
-3 = 2 + b
b = -3 - 2
b = -5
Therefore, the equation in slope intercept form is y = -2x - 5
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Find x in the right triangle. 324−−−√324
B 147−−−√147
C 63−−√63
D 175−−−√175
E 21−−√21
Answer:
I believe it is 3rd one but not 100% sure
Step-by-step explanation:
hope this helps
The number of bagels sold daily for two bakeries is shown in the table:
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median?
A. Mean for both bakeries because the data is symmetric
B. Mean for Bakery B because the data is symmetric; median for Bakery A because the data is not symmetric
C. Mean for Bakery A because the data is symmetric; median for Bakery B because the data is not symmetric
D. Median for both bakeries because the data is not symmetric
It is better to describe the centers of distribution in terms of the
D. Median for both bakeries because the data is not symmetric.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
We know symmetric data sets have a graph that is bell-shaped.
Here the data for both bakeries are not symmetric we can conclude that from the given table itself so it is better to describe the centers of distribution in terms of the median for both bakeries because the data is not symmetric.
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4. Assume a manufacturer makes an item that costs $2.50 to produce. The
markup when sold to the distributor is 35 percent. What is the cost to the
distributor? When the distributor sells the item to the retailer, the markup is 40
percent. How much will the retailer pay for the item?
Answer: Cost to distributer $3.38
Cost to retailer $4.73
Step-by-step explanation: First find 35 percent of $2.50
2.50 x 0.35 = 0.875 this is 35% of 2.50
Then add this amount to 2.50
2.50 + 0.875 = 3.375 or $3.38
Then to find the cost to the retailer repeat this process with 40%
3.38 x 0.40 = 1.352
1.352 + 3.38. = 4.732 or $4.73
(0.5- 0.3) power of 2?
Solving the Question
[tex](0.5- 0.3)^2[/tex]
⇒ Subtract inside the parentheses:
[tex]= (0.2)^2[/tex]
⇒ Evaluate the exponent by multiplying 0.2 by 0.2:
[tex]= 0.04[/tex]
Answer0.04
Answer:
0.04
Step-by-step explanation:
find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = sin(x), a = ????
The taylor series of sin x at x= π is ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
the Taylor series n of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point.
since the function we are given is :
sin(x), since we need to find the Taylor series of sin(x) at x=π, which can also be written as : sin(x+π)
we can find find the Taylor series of sin(x+π) at x=0
sin(x+π)=−sin(x)
= ∑( for n=0,∞) [tex]\frac{(-1)^{n}x^(2n+1) }{(2n+1)!}[/tex]
= ∑( for n=0,∞) [tex]\frac{-1^{n+1}x^{2n+1} }{(2n+1)!}[/tex]
so sin (x)= ∑( for n=0,∞) [tex]\frac{-1^{n+1}(x-\pi )^{2n+1} }{(2n+1)! }[/tex]
To know more about Taylor series refer to the link brainly.com/question/28158012
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find the Taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0.] f(x) = sin(x), a = π????